If $$p(x) = 2x^3 - 12x^2 + 11x - 5$$ , what is $$p(5)$$ ?

$$p(5) = 2(5)^3 - 12(5)^2 + 11(5) - 5 = 0$$ , so 5 is a solution of $$p(x)$$ .

What is the significance of the value of C in the polynomial $$p(x) = 5x^3 + 34x^2 + 26x + C$$ when dividing by $$x + 6$$ ?

The value of C must be such that the remainder is 0 when dividing by $$x + 6$$ , indicating that $$x + 6$$ is a factor of $$p(x)$$ .

What does it mean if a polynomial has a remainder of 33 when evaluated at a certain point?

If a polynomial has a remainder of 33 when evaluated at a point $$c$$ , it means that $$c$$ is not a solution of the polynomial, as $$p(c) ≠ 0$$ .

How can you use the Remainder Theorem to find factors of a polynomial?

By evaluating the polynomial at potential roots (values of $$c$$ ) and checking if the remainder is 0, you can determine if $$x - c$$ is a factor.

What is the relationship between the Remainder Theorem and the Factor Theorem?

The Remainder Theorem provides the remainder of a polynomial division, while the Factor Theorem uses this remainder to determine if a linear factor exists.

If $$p(x) = 2x^3 - 15x + 9$$ , what can you conclude if $$p(3) ≠ 0$$ ?

If $$p(3) ≠ 0$$ , then 3 is not a solution of the polynomial $$p(x)$$ .

What is the first step in synthetic division?

The first step in synthetic division is to write down the coefficients of the polynomial in descending order of the degree.

How do you find the value of C if $$x - 5$$ is a factor of $$p(x) = 2x^3 - 12x^2 + 11x - C$$ ?

Set $$p(5) = 0$$ and solve for C to find the value that makes $$x - 5$$ a factor.

What is the result of synthetic division if the divisor is $$x - c$$ ?

The result of synthetic division will be a polynomial of one degree less than the original polynomial, along with the remainder.

What does it indicate if a polynomial has multiple solutions?

If a polynomial has multiple solutions, it indicates that it can be factored into multiple linear factors, each corresponding to a solution.

Remainder Theorem and Factor Theorem Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Remainder Theorem?

Back

Tags

CCSS.HSA.APR.B.2

2.

FLASHCARD QUESTION

Front

What does it mean if the remainder is 0 when using the Remainder Theorem?

Back

Tags

CCSS.HSA.APR.B.2

3.

FLASHCARD QUESTION

Front

What is the Factor Theorem?

Back

Tags

CCSS.HSA.APR.B.2

4.

FLASHCARD QUESTION

Front

How do you determine if a number is a solution of a polynomial?

Back

Tags

CCSS.6.EE.B.5

5.

FLASHCARD QUESTION

Front

What is synthetic division?

Back

Tags

CCSS.HSA.APR.D.6

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.IF.A.2

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.B.2

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